Math Is Fun Forum

chriss

Member

Registered: 2009-02-08

Posts: 4

i need help!!!

a sequence of natural numbers χ1,χ2,...,χn called:
1) "supertwofold" if for every term of her except the first forces xn+1 > 2xn.
2) "twofold" if for every terms of her except the first forces xn+1=2xn.
3)"half" if for every term of her except the first forces xn+1 < 2xn.
And the question is....are the above sequences numerables?

I have no idea who i'll prove it...so if someone knows please help me.

thanks!!!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: i need help!!!

Hi chriss;

What are numerables?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

chriss

Member

Registered: 2009-02-08

Posts: 4

Re: i need help!!!

i am sorry Countable  i ment.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: i need help!!!

Hi chriss;

For 1)

The recurrence:

is one that satisfies your property of supertwofoldness. The sequence it determines
{1,3,7,15...} is countable or denumerable because each term of the recurrence for n=1,2,3,4... generates 1 and only one element of the sequence. So there is a mapping or one to one correspondence between the set N (natural or counting numbers) and the elements of the sequence.

This is a little rough in terms of jargon, which is not my strongpoint. So go here to get more:

http://en.wikipedia.org/wiki/Countable_set

http://math.suite101.com/article.cfm/co … table_sets

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.